DFA is a bit of a tricky concept, since it's often (mis)used by sports news outlets, broadcasters, and bloggers as a synonym for outrighted, released, or even optioned. However, when a player is DFA'd, or designated for assignment, all it means is that he has been removed from his team's 40-man roster and essentially placed in baseball limbo. His team has 10 days to trade him, release him, or send him outright to a minor league affiliate. When a team wishes instead to release a player, it's usually reported that way initially (e.g. "the Mets released Luis Castillo" as opposed to "the Mets designated Luis Castillo for assignment with the intention of releasing him"). Similarly, when a team comes to terms with another team on a trade, the DFA also typically goes unmentioned.
DFAs tend only to be announced when, either, 1) the team intends to pass the player through waivers and outright him to the minors, or 2) the team needed the roster spot and wants to try to trade the player before trying to pass him through waivers to outright him to the minors. If the team is unable or unwilling to trade the player who has been DFA'd, then the team must request outright waivers. Waivers take a minimum of 47 hours to obtain (e.g. if the player is placed on waivers by 2 pm on Monday, and no one makes a claim, waivers will be obtained at 1 pm on Wednesday). So in order to outright a player who has been DFA'd, waivers have to not only be requested, but obtained by the end of the 10-day window. In some cases, as the Mets did with Chin-lung Hu, the team will pass the player through waivers before he is even DFA'd. The risk here is that he will be claimed and the team will lose a player before his roster spot was even needed. The benefit is that if he clears waivers, he can be outrighted immediately upon being DFA'd, without having to clear waivers at that time.
Ultimately, the DFA is just the way a team clears a spot on its 40-man roster.